Question

The business problem facing the director of broadcasting operations for a television station was the issue of standby hours (i.e hours in which employees at the station are paid but are not actually involved in any activity) and what factors were related to standby hours. The study included the following variables:

Standby Hours (Y)- Total number of standby hours in a week.

Weekly staff count (X₁)- Weekly total of people-days

Remote engineering hours (X₂)- Total number of engineering hours worked by employees at locations away from the central plant.

Data was collected for 26 weeks:

Standby	Total Staff	Remote
245	338	414
177	333	598
271	358	656
211	372	631
196	339	528
135	289	409
195	334	382
118	293	399
116	325	343
147	311	338
154	304	353
146	312	289
115	283	388
161	307	402
274	322	151
245	335	228
201	350	271
183	339	440
237	327	475
175	328	347
152	319	449
188	325	336
188	322	267
197	317	235
261	315	164
232	331	270

a.) state the multiple regression equation (show work)

b.) interpret the meaning of the slopes, b₁ and b₂, in this problem. (show work)

c.)Explain why the regression coefficient, b₀, has no practical meaning in the context of this problem.

d.) Predict the mean standby hours for a week in which the weekly staff recount was 310 people-days and the remote engineering hours total was 400 (SHOW WORK)

e.) what is the p-value and interpret its result? (SHow work)

***Please use In depth Excel or PHStat to verify the answers. showing the steps to doing the problem is very helpful to me so I can better understand how to do the whole process.

Answer 1

Using Excel, go to Data, select Data Analysis, choose Regression. Put Standby in Y input range and Total Staff and Remote in X input range.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.700
R Square	0.490
Adjusted R Square	0.446
Standard Error	35.387
Observations	26
ANOVA
	df	SS	MS	F	Significance F
Regression	2	27662.543	13831.271	11.045	0.000
Residual	23	28802.073	1252.264
Total	25	56464.615
	Coefficients	Standard Error	t Stat	P-value
Intercept	-330.675	116.480	-2.839	0.009
Total Staff	1.765	0.379	4.656	0.000
Remote	-0.139	0.059	-2.363	0.027

a) Standby = -330.675 + 1.765*Total Staff - 0.139*Remote

b) b1: With one unit increase in total staff, standby hours increase by 1.765

b1: With one unit increase in remote engineering hours, standby hours decrease by 0.139 hours

c) b0 signifies that if both weekly staff count and remote hours are zero, standy hours will be -330.675. This is not possible as hours cannot be less than zero.

d) Remote = 400, Total staff = 310

Standby = -330.675 + 1.765*Total Staff - 0.139*Remote\

Standby = -330.675 + 1.765*310 -0.139*400

= 160.875 hours

e) H0: The model is not a good fit

H1: The model is a good fit

p-value (Significance F) = 0.000

Since p-value is less than 0.05, we reject the null hypothesis and conclude that the model is a good fit.